Generalized Linear Models (GLM) in R

The generalized linear models (GLM) can be used when the distribution of the response variable is non-normal or when the response variable is transformed into linearity. The GLMs are flexible extensions of linear models that are used to fit the regression models to non-Gaussian data.

One can classify a regression model as linear or non-linear regression models.

Generalized Linear Models

The basic form of a Generalized linear model is
\begin{align*}
g(\mu_i) &= X_i’ \beta \\
&= \beta_0 + \sum\limits_{j=1}^p x_{ij} \beta_j
\end{align*}
where $\mu_i=E(U_i)$ is the expected value of the response variable $Y_i$ given the predictors, $g(\cdot)$ is a smooth and monotonic link function that connects $\mu_i$ to the predictors, $X_i’=(x_{i0}, x_{i1}, \cdots, x_{ip})$ is the known vector having $i$th observations with $x_{i0}=1$, and $\beta=(\beta_0, \beta_1, \cdots, \beta_p)’$ is the unknown vector of regression coefficients.

Fitting Generalized Linear Models

The glm() is a function that can be used to fit a generalized linear model, using the generic form of the model below. The formula argument is similar to that used in the lm() function for the linear regression model.

mod <- glm(formula, family = gaussian, data = data.frame)

The family argument is a description of the error distribution and link function to be used in the model.

The class of generalized linear models is specified by giving a symbolic description of the linear predictor and a description of the error distribution. The link functions for different families of the probability distribution of the response variables are given below. The family name can be used as an argument in the glm( ) function.

Family NameLink Functions
binomiallogit , probit, cloglog
gaussianidentity, log, inverse
Gammaidentity, inverse, log
inverse gaussian$1/ \mu^2$, identity, inverse,log
poissonlogit, probit, cloglog, identity, inverse
quasilog, $1/ \mu^2$, sqrt

Generalized Linear Models Example in R

Consider the “cars” dataset available in R. Let us fit a generalized linear regression model on the data set by assuming the “dist” variable as the response variable, and the “speed” variable as the predictor. Both the linear and generalized linear models are performed in the example below.

data(cars)
head(cars)
attach(cars)

scatter.smooth(x=speed, y=dist, main = "Dist ~ Speed")

# Linear Model
lm(dist ~ speed, data = cars)
summary(lm(dist ~ speed, data = cars)

# Generalized Linear Model
glm(dist ~ speed, data=cars, family = "gaussian")
plot(glm(dist ~ speed, data = cars))
summary(glm(dist ~ speed, data = cars))
Generalized Linear Models

Diagnostic Plots of Generalized Linear Models

generalized linear models

https://gmstat.com

Important R Language MCQs ggplot2 with Answers 8

The quiz “R Language MCQS ggplot2” will help you check your ability to execute some basic operations on objects in the R language, and it will also help you understand some basic concepts. This quiz may also improve your computational understanding.

Quiz about R Language

1. How sampling with and without replacement can be done using R?

 
 
 
 

2. Which is the R command for obtaining 1000 random numbers through normal distribution with mean 0 and variance 1?

 
 
 
 

3. Let us have 1000 random samples of size 6 under SRSWOR using the following population (111, 150, 121, 198, 112, 136, 114, 129, 117, 115, 186, 110, 121, 115, 114) which is the R command for repeating this procedure 1500 times?

 
 
 
 

4. Which of the following are standards of tidy data?

 
 
 
 

5. Which summary functions can you use to preview data frames in R Language?

 
 
 
 

6. You are cleaning a data frame with improperly formatted column names. To clean the data frame you want to use the clean_names() function. Which column names will be changed using the clean_names() with default parameters?

 
 
 
 

7. Data analysts are cleaning their data in R. They want to be sure that their column names are unique and consistent to avoid any errors in their analysis. What R function can they use to do this automatically?

 
 
 
 

8. When programming in R, what is a pipe used as an alternative for?

 
 
 
 

9. Which R function can be used to make changes to a data frame?

 
 
 
 

10. For the population y<-c(1,2,3,4,5), write the R command to find the mean?

 
 
 
 

11. A data analyst is working with the penguin’s data. They write the following code:
penguins %>%

The variable species includes three penguin species: Adelie, Chinstrap, and Gentoo. What code chunk does the analyst add to create a data frame that only includes the Gentoo species?

 
 
 
 

12. Data analysts are working with customer information from their company’s sales data. The first and last names are in separate columns, but they want to create one column with both names instead. Which of the following functions can they use?

 
 
 
 

13. What is the class of the object defined by the expression? x <- c(4,5,10)?

 

 
 
 
 

14. Suppose you want to simulate a coin toss 20 times in R. Write the command.

 
 
 
 

15. In R the following are all atomic data types EXCEPT:

 
 
 
 

16. Why are tibbles a useful variation of data frames?

 
 
 
 

17. For the population y<-c(1,2,3,4,5), write the R command to find the median?

 

 
 
 
 

18. In ggplot2, an _____ is a visual property of an object in your plot.

 
 
 
 

19. A data scientist is trying to print a data frame but when you print the data frame to the console output produces too many rows and columns to be readable. What could they use instead of a data frame to make printing more readable?

 
 
 
 

20. Write the R commands for generating 700 random variables from normal distribution by using the following information: Mean = 14, SD = 3, n = 5, k = 2000.

 
 
 
 

Frequently Asked Questions About R Language MCQs ggplot2

R Language MCQs ggplot2 Function

  • What is the class of the object defined by the expression? x <- c(4,5,10)?  
  • In R the following are all atomic data types EXCEPT:
  • For the population y<-c(1,2,3,4,5), write the R command to find the mean.
  • For the population y<-c(1,2,3,4,5), write the R command to find the median.
  • Let us have 1000 random samples of size 6 under SRSWOR using the following population (111, 150, 121, 198, 112, 136, 114, 129, 117, 115, 186, 110, 121, 115, 114) which is the R command for repeating this procedure 1500 times?
  • Which is the R command for obtaining 1000 random numbers through normal distribution with mean 0 and variance 1?
  • How sampling with and without replacement can be done using R?
  • Write the R commands for generating 700 random variables from normal distribution by using the following information: Mean = 14, SD = 3, n = 5, k = 2000.
  • Suppose you want to simulate a coin toss 20 times in R. Write the command.
  • When programming in R, what is a pipe used as an alternative for?
  • Which of the following are standards of tidy data?
  • Which summary functions can you use to preview data frames in R Language?
  • Which R function can be used to make changes to a data frame?
  • Why are tibbles a useful variation of data frames?
  • Data analysts are cleaning their data in R.
  • They want to be sure that their column names are unique and consistent to avoid any errors in their analysis. What R function can they use to do this automatically?
  • Data analysts are working with customer information from their company’s sales data. The first and last names are in separate columns, but they want to create one column with both names instead. Which of the following functions can they use?
  • A data scientist is trying to print a data frame but when you print the data frame to the console output produces too many rows and columns to be readable. What could they use instead of a data frame to make printing more readable?
  • A data analyst is working with the penguin’s data. They write the following code: penguins %>% The variable species includes three penguin species: Adelie, Chinstrap, and Gentoo. What code chunk does the analyst add to create a data frame that only includes the Gentoo species?
  • You are cleaning a data frame with improperly formatted column names. To clean the data frame you want to use the clean_names() function. Which column names will be changed using the clean_names() with default parameters?
  • In ggplot2, an ———- is a visual property of an object in your plot.

R Language MCQs 2

Computer MCQs Online Test

9 Ways to Get Help in R Language

In this article, we will discuss 9 ways to get help in R Language. R Language has a very useful and advanced help system that helps the R user to understand the R language and lets him know how programming should be done in the R language.

Get Help in R Language

To get help in R language you need to click the Help button on the toolbar of RGui (R Graphical User Interface) windows. If you have internet access on your PC you can type CRAN in Google and search for the help you need at CRAN.

Use of “?” for Help

On the other hand, if you know the name of the function, you need to type the question mark (?) followed by the name of the required function on the R command line prompt. For example to get help about “lm” function type ?lm and then press the ENTER key from the keyboard.
help(lm) or ?lm have the same search results in the R language.

help.start()

Getting General help in R write the following command at the R command prompt

help.start()

## Output
help.start()
starting httpd help server ... done
If nothing happens, you should open
‘http://127.0.0.1:13825/doc/html/index.html’ yourself
9 ways to get help in R Language

Sometimes it is difficult to remember the precise name of the function, but you know the subject on which you need help for example data input. Use the help.search function (without question mark) with your query in double quotes like this:

help.search("data input")

Press the ENTER key, you will see the names of the R functions associated with the query.  After that, you can easily use ?lm to get help in R.

Use of find(” “)

Getting help in R, find, and apropos are also useful functions. The find function tells you what package something is in: for example

find("cor") gives output that the cor in the stats package.

Use of apropos()

The apropos function returns a character vector giving the names of all objects in the search list that match your inquiry (potentially partial) i.e., this command lists all functions containing your string. For example

apropos("lm")

will give the list of all functions containing the string lm

Use of example()

example(lm) will provide an example of your required function that is in this case, an example of the function lm()

Online Help

There is a huge amount of information about R on the web. On CRAN you will find a variety of help/ manuals. There are also answers to FAQs (Frequently Asked Questions) and R News (contains interesting articles, book reviews, and news of forthcoming releases. The search facility of the site allows you to investigate the contents of the R documents, functions, and searchable mail archives.

You can search your required function or string in help manuals and archived mailing lists by using

RSiteSearch("read.csv")

Get Vignettes

vignette is an R jargon for documentation and is written in the spirit of sharing knowledge, and
assisting new users in learning the purpose and use of a package. To get some help in R try ?vignette. Vignettes are optional supplemental documentation, that’s why not all packages come with vignettes.

vignette()          # will show available vignettes
vignette("foo")     # will show specific vignette

Now you have learned about getting help in R, now you can continue with the other R tutorials. It is possible that you do not understand something discussed in the coming R tutorials. If this happens then you should use the built-in help system before going to the internet. In most cases, the help system of R Language will give you enough information about the required function that you have searched for.

Some Sources of R Help/ Manual/ Documentations

https://cran.r-project.org/manuals.html

https://cran.r-project.org/other-docs.html

https://www.r-project.org/help.html

https://cran.r-project.org/bin/windows/base/rw-FAQ.html